A well known sufficient condition for the mean residual life order of two random variables is the hazard rate order of the two random variables. The hazard rate order is characterized by the monotonicity of the ratio of the two survival functions. However in many cases this ratio is non monotone...

In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k−1 (jk) components have failed by time t....

Let X1,…,Xn (Y1,…,Yn) be independent random variables such that Xi (Yi) follows the gamma distribution with shape parameter α and mean αλi(αμi), α0,λi0 (μi0), i=1,…,n. Let λ=(λ1,…,λn), μ=(μ1,…,μn) and let r̃n:n(λ;x) (r̃n:n(μ;x)) denote the reversed hazard rate of...

Let X1,X2, and X3 be independent random variables with absolutely continuous distributions having the common support [0,∞). We show that if X1≤hr[mrl,lr]X3 and X2≤hr[mrl,lr]X3, then max{X1,X2}≤hr[mrl,lr]max{X1,X3}. We also show that if X2≤rh[lr]X1 and X2≤rh[lr]X3, then...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

Purpose The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented. Design/methodology/approach First, Glaser’s...